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Title: Graph-functions associated with an edge-property
Authors: Dong, Fengming
Hendy, Michael
Teo, Kee Leong
Little, Charles H. C.
Issue Date: 2004
Citation: Dong, F., Hendy, M., Teo, K. L., & Little, C. H. C. (2004). Graph-functions associated with an edge-property. Australasian Journal of Combinatorics, 30, 3-20.
Abstract: Let P be an edge-property of graphs. For any graph G we construct a polynomial Ψ(G, η,P), in an indeterminate η, in which the coefficient of ηr for any r ≥ 0 gives the number of subsets of E(G) that have cardinality r and satisfy P. An example is the well known matching polynomial of a graph. After studying the properties of Ψ(G, η,P) in general, we specialise to two particular edge-properties: that of being an edge-covering and that of inducing an acyclic subgraph. The resulting polynomials, called the edge-cover and acyclic polynomials respectively, are studied and recursive formulae for computing them are derived. As examples we calculate these polynomials for paths and cycles.
ISSN: 1034-4942
Appears in Collections:Journal Articles

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